On the nature of three-dimensional encoding in the cognitive map: Commentary on Hayman, Verriotis, Jovalekic, Fenton, and Jeffery

Path integration in a three-dimensional world: the case of desert ants

Desert ants use path integration to return from foraging excursions on a shortcut way to their nests. Intriguingly, when walking over hills, the ants incorporate the ground distance, the paths’ projection to the horizontal plane, into their path integrator. This review discusses how Cataglyphis may solve this computational feat. To infer ground distance, ants must incorporate the inclination of path segments into the assessment of distance. Hair fields between various joints have been eliminated as likely sensors for slope measurement, without affecting slope detection; nor do postural adaptations or changes in gait provide the relevant information. Changes in the sky’s polarization pattern due to different head inclinations on slopes were ruled out as cues. Thus, the mechanisms by which ants may measure slopes still await clarification. Remarkably, the precision of slope measurement is roughly constant up to a 45° inclination, but breaks down at 60°. An encounter of sloped path segments during a foraging trip induces a general acceptance of slopes, however, slopes are not associated with specific values of the home vector. All current evidence suggests that Cataglyphis does not compute a vector in 3-D: path integration seems to operate exclusively in the horizontal plane.

The Brain Compass: A Perspective on How Self-Motion Updates the Head Direction Cell Attractor

Head direction cells form an internal compass signaling head azimuth orientation even without visual landmarks. This property is generated by a neuronal ring attractor that is updated using rotation velocity cues. The properties and origin of this velocity drive remain, however, unknown. We propose a quantitative framework whereby this drive represents a multisensory self-motion estimate computed through an internal model that uses sensory prediction errors of vestibular, visual, and somatosensory cues to improve on-line motor drive. We show how restraint-dependent strength of recurrent connections within the attractor can explain differences in head direction cell firing between free foraging and restrained passive rotation. We also summarize recent findings on how gravity influences azimuth coding, indicating that the velocity drive is not purely egocentric. Finally, we show that the internal compass may be three-dimensional and hypothesize that the additional vertical degrees of freedom use global allocentric gravity cues.

Hippocampal place cell encoding of sloping terrain

Effective navigation relies on knowledge of one's environment. A challenge to effective navigation is accounting for the time and energy costs of routes. Irregular terrain in ecological environments poses a difficult navigational problem as organisms ought to avoid effortful slopes to minimize travel costs. Route planning and navigation have previously been shown to involve hippocampal place cells and their ability to encode and store information about an organism's environment. However, little is known about how place cells may encode the slope of space and associated energy costs as experiments are traditionally carried out in flat, horizontal environments. We set out to investigate how dorsal-CA1 place cells in rats encode systematic changes to the slope of an environment by tilting a shuttle box from flat to 15 ° and 25 ° while minimizing external cue change. Overall, place cell encoding of tilted space was as robust as their encoding of flat ground as measured by traditional place cell metrics such as firing rates, spatial information, coherence, and field size. A large majority of place cells did, however, respond to slope by undergoing partial, complex remapping when the environment was shifted from one tilt angle to another. The propensity for place cells to remap did not, however, depend on the vertical distance the field shifted. Changes in slope also altered the temporal coding of information as measured by the rate of theta phase precession of place cell spikes, which decreased with increasing tilt angles. Together these observations indicate that place cells are sensitive to relatively small changes in terrain slope and that terrain slope may be an important source of information for organizing place cell ensembles. The terrain slope information encoded by place cells could be utilized by efferent regions to determine energetically advantageous routes to goal locations.

Three-dimensional tuning of head direction cells in rats

Head direction (HD) cells fire when the animal faces that cell's preferred firing direction (PFD) in the horizontal plane. The PFD response when the animal is oriented outside the earth-horizontal plane could result from cells representing direction in the plane of locomotion or as a three-dimensional (3D), global-referenced direction anchored to gravity. To investigate these possibilities, anterodorsal thalamic HD cells were recorded from restrained rats while they were passively positioned in various 3D orientations. Cell responses were unaffected by pitch or roll up to ~90° from the horizontal plane. Firing was disrupted once the animal was oriented >90° away from the horizontal plane and during inversion. When rolling the animal around the earth-vertical axis, cells were active when the animal's ventral surface faced the cell's PFD. However, with the rat rolled 90° in an ear-down orientation, pitching the rat and rotating it around the vertical axis did not produce directionally tuned responses. Complex movements involving combinations of yaw-roll, but usually not yaw-pitch, resulted in reduced directional tuning even at the final upright orientation when the rat had full visual view of its environment and was pointing in the cell's PFD. Directional firing was restored when the rat's head was moved back-and-forth. There was limited evidence indicating that cells contained conjunctive firing with pitch or roll positions. These findings suggest that the brain's representation of directional heading is derived primarily from horizontal canal information and that the HD signal is a 3D gravity-referenced signal anchored to a direction in the horizontal plane. NEW & NOTEWORTHY This study monitored head direction cell responses from rats in three dimensions using a series of manipulations that involved yaw, pitch, roll, or a combination of these rotations. Results showed that head direction responses are consistent with the use of two reference frames simultaneously: one defined by the surrounding environment using primarily visual landmarks and a second defined by the earth's gravity vector.

Anisotropy of Human Horizontal and Vertical Navigation in Real Space: Behavioral and PET Correlates

Spatial orientation was tested during a horizontal and vertical real navigation task in humans. Video tracking of eye movements was used to analyse the behavioral strategy and combined with simultaneous measurements of brain activation and metabolism ([18F]-FDG-PET). Spatial navigation performance was significantly better during horizontal navigation. Horizontal navigation was predominantly visually and landmark-guided. PET measurements indicated that glucose metabolism increased in the right hippocampus, bilateral retrosplenial cortex, and pontine tegmentum during horizontal navigation. In contrast, vertical navigation was less reliant on visual and landmark information. In PET, vertical navigation activated the bilateral hippocampus and insula. Direct comparison revealed a relative activation in the pontine tegmentum and visual cortical areas during horizontal navigation and in the flocculus, insula, and anterior cingulate cortex during vertical navigation. In conclusion, these data indicate a functional anisotropy of human 3D-navigation in favor of the horizontal plane. There are common brain areas for both forms of navigation (hippocampus) as well as unique areas such as the retrosplenial cortex, visual cortex (horizontal navigation), flocculus, and vestibular multisensory cortex (vertical navigation). Visually guided landmark recognition seems to be more important for horizontal navigation, while distance estimation based on vestibular input might be more relevant for vertical navigation.

3-D spatial memory and navigation: functions and disorders

PURPOSE OF REVIEW

The aim of this review is to report on the specialized neuronal systems mediating spatial orientation and navigation discovered in animal experiments. These findings have important implications for the clinical management of patients with vestibular disorders or dementia and for translational research in these fields.

RECENT FINDINGS

The following anatomically and functionally separate, but nevertheless cooperative cell types have been characterized: angular head velocity cells and head direction cells, which depend on vestibular input and interact with place cells and grid cells, which represent position and distance. The entire system is thought to encode internal cognitive maps whose spatial data can be utilized for navigation and orientation. Flying and swimming species use spatial orientation and navigation isotropically, i.e., in the earth-horizontal and vertical directions, whereas ground-based species, including humans, perform better in the earth-horizontal plane (anisotropically). Examples of clinical disorders with deficits of spatial orientation and navigation are bilateral peripheral vestibulopathy, mild cognitive impairment, and dementia.

SUMMARY

Testing spatial orientation and navigation should become an integral part of routine neurological examinations, especially in the elderly. Also desirable are the further development and standardization of simple and reliable smart phone-based bedside tests to measure these functions in patients.

"Taller and Shorter": Human 3-D Spatial Memory Distorts Familiar Multilevel Buildings

Animal experiments report contradictory findings on the presence of a behavioural and neuronal anisotropy exhibited in vertical and horizontal capabilities of spatial orientation and navigation. We performed a pointing experiment in humans on the imagined 3-D direction of the location of various invisible goals that were distributed horizontally and vertically in a familiar multilevel hospital building. The 21 participants were employees who had worked for years in this building. The hypothesis was that comparison of the experimentally determined directions and the true directions would reveal systematic inaccuracy or dimensional anisotropy of the localizations. The study provides first evidence that the internal representation of a familiar multilevel building was distorted compared to the dimensions of the true building: vertically 215% taller and horizontally 51% shorter. This was not only demonstrated in the mathematical reconstruction of the mental model based on the analysis of the pointing experiments but also by the participants’ drawings of the front view and the ground plan of the building. Thus, in the mental model both planes were altered in different directions: compressed for the horizontal floor plane and stretched for the vertical column plane. This could be related to human anisotropic behavioural performance of horizontal and vertical navigation in such buildings.

Neural encoding of large-scale three-dimensional space-properties and constraints

How the brain represents represent large-scale, navigable space has been the topic of intensive investigation for several decades, resulting in the discovery that neurons in a complex network of cortical and subcortical brain regions co-operatively encode distance, direction, place, movement etc. using a variety of different sensory inputs. However, such studies have mainly been conducted in simple laboratory settings in which animals explore small, two-dimensional (i.e., flat) arenas. The real world, by contrast, is complex and three dimensional with hills, valleys, tunnels, branches, and—for species that can swim or fly—large volumetric spaces. Adding an additional dimension to space adds coding challenges, a primary reason for which is that several basic geometric properties are different in three dimensions. This article will explore the consequences of these challenges for the establishment of a functional three-dimensional metric map of space, one of which is that the brains of some species might have evolved to reduce the dimensionality of the representational space and thus sidestep some of these problems.

The self-organization of grid cells in 3D

Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively quickly, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering.

Decoding signal processing in thalamo-hippocampal circuitry: implications for theories of memory and spatial processing

A major tool in understanding how information is processed in the brain is the analysis of neuronal output at each hierarchical level through which neurophysiological signals are propagated. Since the experimental brain operation performed on Henry Gustav Molaison (known as patient H.M.) in 1953, the hippocampal formation has gained special attention, resulting in a very large number of studies investigating signals processed by the hippocampal formation. One of the main information streams to the hippocampal formation, vital for episodic memory formation, arises from thalamo-hippocampal projections, as there is extensive connectivity between these structures. This connectivity is sometimes overlooked by theories of memory formation by the brain, in favour of theories with a strong cortico-hippocampal flavour. In this review, we attempt to address some of the complexity of the signals processed within the thalamo-hippocampal circuitry. To understand the signals encoded by the anterior thalamic nuclei in particular, we review key findings from electrophysiological, anatomical, behavioural and computational studies. We include recent findings elucidating the integration of different signal modalities by single thalamic neurons; we focus in particular on the propagation of two prominent signals: head directionality and theta rhythm. We conclude that thalamo-hippocampal processing provides a centrally important, substantive, and dynamic input modulating and moderating hippocampal spatial and mnemonic processing. This article is part of a Special Issue entitled SI: Brain and Memory.

Resolving the active versus passive conundrum for head direction cells

Head direction (HD) cells have been identified in a number of limbic system structures. These cells encode the animal's perceived directional heading in the horizontal plane and are dependent on an intact vestibular system. Previous studies have reported that the responses of vestibular neurons within the vestibular nuclei are markedly attenuated when an animal makes a volitional head turn compared to passive rotation. This finding presents a conundrum in that if vestibular responses are suppressed during an active head turn how is a vestibular signal propagated forward to drive and update the HD signal? This review identifies and discusses four possible mechanisms that could resolve this problem. These mechanisms are: (1) the ascending vestibular signal is generated by more than just vestibular-only neurons, (2) not all vestibular-only neurons contributing to the HD pathway have firing rates that are attenuated by active head turns, (3) the ascending pathway may be spared from the affects of the attenuation in that the HD system receives information from other vestibular brainstem sites that do not include vestibular-only cells, and (4) the ascending signal is affected by the inhibited vestibular signal during an active head turn, but the HD circuit compensates and uses the altered signal to accurately update the current HD. Future studies will be needed to decipher which of these possibilities is correct.

Representation of three-dimensional space in the hippocampus of flying bats

Many animals, on air, water, or land, navigate in three-dimensional (3D) environments, yet it remains unclear how brain circuits encode the animal's 3D position. We recorded single neurons in freely flying bats, using a wireless neural-telemetry system, and studied how hippocampal place cells encode 3D volumetric space during flight. Individual place cells were active in confined 3D volumes, and in >90% of the neurons, all three axes were encoded with similar resolution. The 3D place fields from different neurons spanned different locations and collectively represented uniformly the available space in the room. Theta rhythmicity was absent in the firing patterns of 3D place cells. These results suggest that the bat hippocampus represents 3D volumetric space by a uniform and nearly isotropic rate code.